What is 36x^2+8y^2=98 ?

The solution to 36x^2+8y^2=98 is Ellipse with (h,k)=(0,0),a= 7/(3sqrt(2)),b= 7/2

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36x^2+8y^2=98

36 x^{2} + 8 y^{2} = 98

(h, k) = (0, 0), a = \frac{7}{3 2}, b = \frac{7}{2}

Solution steps

36 x^{2} + 8 y^{2} = 98

Rewrite

36 x^{2} + 8 y^{2} = 98

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{7}{3 2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{7}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{7}{3 2}, b = \frac{7}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{7}{2}, a = \frac{7}{3 2}

(\frac{y}{8})^{2} + (\frac{x}{7})^{2} = 1

\frac{x ^{2}}{64} + \frac{y ^{2}}{9} = 1

\frac{( x - 4 ) ^{2}}{36} + \frac{( y - 2 ) ^{2}}{6} - 1 = 0

8 x^{(2)} + 2 y^{(2)} + 16 x = 0

2 x^{2} + 5 y^{2} + 3 x + 30 y - 16 = 0

What is 36x^2+8y^2=98 ?
The solution to 36x^2+8y^2=98 is Ellipse with (h,k)=(0,0),a= 7/(3sqrt(2)),b= 7/2